\(a,3^2\cdot\frac{1}{243}=3^2\cdot\frac{1}{3^5}=\frac{1}{3^3}=\frac{1^3}{3^3}=\left(\frac{1}{3}\right)^3\)
\(b,81^2\cdot\frac{1}{3^3}=\left(3^4\right)^2\cdot\frac{1}{3^3}=3^8\cdot\frac{1}{3^3}=3^5\)
a) \(3^2.\frac{1}{243}=\frac{1.3^3}{243}=\frac{3^2}{243}=\frac{3^2}{3^5}=\frac{1}{3^3}=\frac{1}{27}\)
b) \(81^2.\frac{1}{3^3}=\frac{1.81^2}{3^3}=\frac{81^2}{3^3}=\frac{3^8}{3^3}=3^5=243\)